Rajmund Zieliński was a multiple national champion in both road and track cycling. In 1964, he won the Tour de Pologne, with him being awarded a refrigerator for his victory. During the 1960s, he raced in five editions of the Peace Race, winning a total of three stages. He became the first Polish cyclist to win an individual time trial stage of the race. At the 1964 Tokyo Olympics, Zieliński competed in the road race and team time trial events. Four years later, at the 1968 Mexico City Olympics, he competed in two track cycling events. The following year, he competed at both the road and track cycling world championships in Brno.